Block Boundary Value Methods Applied To Neutral Differential Equations With Piecewise Constant Argument

With the further research of neutral differential equations,some researchers have paid attention on neutral functional differential equations.However,there is few research on neutral differential equations with piecewise constant argument.That's why this paper mainly studies the convergence and stability of the block boundary value methods,which successfully solve the neutral differential equations with piecewise constant argument.In the first chapter,we reviewed the research achievements of block boundary value methods and neutral differential equations.The core concepts of boundary value methods and block boundary value methods for the initial problems were introduced in details.In the second chapter,the schemes of block boundary value methods for neutral differential equations with piecewise constant argument are given.Under the classic Lipschitz condition,a convergence theorem has been derived,which proved that the numerical solution of block boundary value methods could be converged.The third chapter is concerned with numerical stability.On the one hand,the stability of block boundary value methods for linear neutral differential equations with piecewise constant argument is investigated and the stability domain of the analytical solution is provided.Subsequently,we consider the stability of nonlinear situation.On the other hand,under the Lipschitz condition,we obtain a sufficient theorem related to stability of block boundary value methods for nolinear neutral differential equations with piecewise constant argument.In the fourth chapter,we have conducted a series of numerical experiments,where four kind of orders is utilized to verify the convergence and stability of block boundary value methods.The outcomes of numerical experiments are consistent with the theoretical analysis mentioned above.